First slide

Different type of processes

Question

During an adiabatic process, the cube of the pressure is found to be inversely proportional to the fourth
power of the volume. Then, the ratio of specific heats is

Moderate

A

1
B

1.33
C

1.67
D

1.4

Solution

Equation of an adiabatic process is $p V^{γ} = k$ …(i)
Given, $p^{3} = \frac{k}{V^{4}}$
$\Rightarrow p^{3} V^{4} = k or p V^{4 / 3} = k$
Comparing Eqs. (i) and (ii), we get
$γ = \frac{4}{3} = 1.33$

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